Basis set dual family

Also, apart from the compilation of dual family basis sets for the series potassium to element (118) [30], and the Universal Gaussian Basis of Malli et al. [26], there are few extensive series for the heavier elements which can be explored for systematic investigations. Among the tasks that need to be undertaken is a more complete derivation of higher quality basis sets, including polarization and correlation functions, and a systematic investigation of even-tempered basis sets. 

A fundamental characteristic of the FPA is the dual extrapolation to the one-and n-particle electronic-structure limits. The process leading to these limits can be described as follows (a) use families of basis sets, such as the correlation-consistent (aug-)cc-p(wC)VnZ sets [51,52], which systematically approach completeness through an increase in the cardinal number n (b) apply lower levels of theory with extended [53] basis sets (typically direct Hartree-Fock (HF) [54] and second-order Moller-Plesset (MP2) [55] computations) (c) use higher-order valence correlation treatments [CCSD(T), CCSDTQ(P), even FCI] [5,56] with the largest possible basis sets and (d) lay out a two-dimensional extrapolation grid based on the assumed additivity of correlation increments followed by suitable extrapolations. FPA assumes that the higher-order correlation increments show diminishing basis set dependence. Focal-point [2,49,50,57-62] and numerous other theoretical studies have shown that even in systems without particularly heavy elements, account must also be taken for core correlation and relativistic phenomena, as well as for (partial) breakdown of the BO approximation, i.e., inclusion of the DBOC correction [28-33]. 

The discussion above applies to uncontracted basis sets. Contracted basis sets present a few further problems. To properly represent the spin-orbit splitting, the two spin-orbit components should be contracted separately. The contraction is now j -dependent, rather than f-dependent, and can only be represented directly in a 2-spinor basis. The problem is not now confined to the small component. If the large-component scalar basis set includes contractions for both spin-orbit components, the product of the contracted basis functions for each spin-orbit component with the spin functions generates a representation for both spin-orbit components. Thus there is a duplication of the basis set that is close to linearly dependent, and some kind of scheme to project out linearly dependent components, either numerically or by conversion to a 2-spinor basis, is mandatory. The same applies to the small component. For example, the contracted p sets for the large-component and d sets both span the same space, but because of the contraction the (i-generated set cannot be made a subset of the -generated set, even if a dual family basis set is used. 

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